Mathematics Home / Research Seminars: Graduate Student Colloquium
Time & Location: All talks are on Tuesdays in Stanley Thomas 316 at 5:00 PM unless otherwise noted.
Organizer: Bisui, Sankhaneel
Title: Counting Lattice Points in Reflexive Polygons
Corey Wolfe | Tulane University
Abstract: The study of toric varieties contains elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology. In this talk, we explore one of those connections mysteriously relating the number of lattice points lying on the boundary of a reflexive polygon and the number of lattice points lying on the boundary of its dual to the number 12. Using the cohomology theory of sheaves on toric surfaces, we hope to demystify the appearance of the number 12.
Title: MTW Sums
Kristina Vandusen | Tulane University
Abstract:
Mordell-Tornheim-Witten sums are an interesting extension of the Riemann zeta function which appears in the evaluation of log gamma integrals. In this talk, I will give an overview of MTW sums and their special cases, and some relations of MTW sums to other known special functions.
Title: How to Give a (good) Math Talk
Robyn Brooks | Tulane University
Abstract:
Giving a research talk is an important part of any mathematics career, but preparing a good math talk can be daunting. In this colloquium, we will discuss what exactly makes a talk “good”. I will also give suggestions and tips on how to best prepare, practice, and execute a good math talk.
Title: Quantum Computing: Teleportation, Zombie Cats, and Spooky Action at a Distance
Zachary Bradshaw | Tulane University
Abstract:
Quantum computing is a computation model that abuses the properties of superposition and entanglement in quantum mechanics, often making it possible to construct algorithms which solve problems faster than a classical computer can. One example of this is Shor’s algorithm, which theoretically factors integers much faster than any known classical algorithm. If a quantum computer capable of implementing Shor’s algorithm is ever built, it will break much of modern encryption. In this talk, I attempt to demystify quantum computing, starting from Schrödinger’s cat and quantum entanglement, which Einstein called “Spooky action at a distance”, and ending with an interesting example referred to as, “Quantum teleportation”.
Title: Getting a handle on the derivation of the Navier-Stokes equations
Dana Ferranti | Tulane University
Abstract:
In applied mathematics, there is always some distance between what the mathematician cares about and what a person directly involved in the field cares about. For example, an applied mathematician may care about existence/uniqueness of solutions of a differential equation but may have no interest in understanding the derivation of the differential equation itself. Because of this difference, I have found few satisfying derivations of the Navier-Stokes equations in mathematical fluid dynamics books. In this talk, I will explain in simple terms the key ideas necessary in understanding where these equations come from. In particular, I will discuss the Cauchy stress tensor and the assumptions underlying the constitutive equations for viscous fluid flow.
Title: Shape Reconstruction and Comparison
Sushovan Majhi | Tulane University
Abstract:
Most of the modern technologies at our service rely on "shapes" in some way or other. Be it the Google Maps showing you the fastest route to your destination eluding a crash or the 3D printer on your desk creating an exact replica of a relic; shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. With the advent of modern sampling technologies, shape reconstruction and comparison techniques have matured profoundly over the last decade.
We will eat pizza and talk about the topological techniques we developed for reconstruction and comparison of Euclidean shapes. We will also demonstrate the software that implements our algorithm.
Title: We will present context and the key ideas from the proof of the Sensitivity Theorem.
Victor Bankston | Tulane University
Abstract:
We will present context and the key ideas from the proof of the Sensitivity Theorem.
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Thanksgiving
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